Statistical evaluation of dead time effects and pulse pileup in fast photon counting. Introduction of the sequential model

Abstract

Corrections to photocount distributions due to dead-thne effects are evaluated by the use of a new pulse-plleup model Incorporating a paralyzable portion and nonparalyzable component In sequence. In the simple model, the two dead times are regarded as nonvarying. A more complete model Is presented In the Appendix, which Incorporates dead times that are themselves random variables.1121 amplifier discriminator and a Model 1109 photon counter) and suggest that the counting system can be considered to be composed of four simplified parts: a detector (including the diode string), an amplifier discriminator, a pulse shaper (within the amplifier discriminator), and a counter. We propose that the detector and amplifier discriminator are both paralyzable systems and can be represented by a single rate-limiting paralyzable counting mechanism. The pulse shaper and counter have electronic components that are nonparalyzable and slower than the previous circuits. They can be represented by a single, rate-limiting nonparalyzable mechanism. The pulse-pileup effects can then be derived for the two sequential systems, each with its own dead time (see also ref 6).

Spatially and temporally resolved measurements of NO<sub>x</sub> fluxes by airborne eddy-covariance over Greater London

“…Instrument precision was quantified by assessing the dark count noise on each PMT, through sampling zero-air (Lee et al, 2009). Photon counting is a well-established technique, with rates following a Poisson distribution (Ingle and Crouch, 1972;Williamson et al, 1988). Allan variance analysis (Werle, 2011) of 1 hour of 'zero-air' data, gave a 2σ precision (limit of detection) for NO and NO2 of 49 and 78 pptv, at an integration period of 9 Hz.…”

Hardware simulator for optical correlation spectroscopy with Gaussian statistics and arbitrary correlation functions

“…Equation (14) shows that σ 2 z and σ 2 y are related to each other by the factor G h (0) △t, which can be easily computed. Indeed, since G h (0) = ∆t ∑ h 2 j and, ∆t ∑ h j = 1, we can write (15) or, in terms of the first two moments of h, as…”

“…Note that a further increase of the count rate would be troublesome because pile up effects [15] would become dominant and affect both the count rate and the statistics of the pulse stream delivered by the board. An example of this effect is shown below.…”

“…4(a Finally, we discuss the main limitation of the hardware simulator, which is related to the maximum output count rate the simulator can deliver. As mentioned in Sect.3, the time resolution of the of the PCI-6534 board is ∆t = 50ns, meaning that, if two or more pulses are closer than 50ns pile up effects [15] take places and only a single pulse is output on the port. Thus, if ⟨I⟩ is the true pulse count rate, the effective count rate delivered by the board is smaller and, for ∆t ⟨I⟩ ≪ 1, can be approximated by ⟨I⟩ ef f ∼ ⟨I⟩ [1 − ∆t ⟨I⟩] [15].…”

Development of a Technique to Simultaneously Verify Linear Energy Transfer and Absorbed Dose in Therapeutic Proton Beams

“…Note that the dose response data has been corrected for PMT dead time (Williamson et al 1988). This is typically a minor effect, but it can reduce the PMT counts by as much as 6% at the highest dose studied (500 Gy), depending on the readout protocol.…”